As a motorist traveling regularly up and down between Dunedin
and Christchurch, I have often pondered the question of how
long a rest stop one would need to avoid ever catching up
again with the oversize traffic ahead. For example, I recently
became stuck behind a line of sheep truck, milk tanker, private
car and a truck and trailer unit. The convoy speed was 80 to
100kph. The vehicles were too close together to pass individually.
Fortunately, they all passed the Waimate turn-off cafe, so I
stopped for a coffee. Sure enough, I didn't catch up with them
again. Assuming that all were traveling to the same destination,
is there an underlying rule of thumb about the time I need to
stop for to ensure I don't get held up again?

Astrid an Huef, a mathematician at the University of Otago, responded.

Let's assume that there is not too much variation in the speed
of the convoy, and that its average speed is s km/hour. Since
we don't encourage speeding, let's assume that you want to travel
only 5km/hour faster than the convoy.

Average speed is distance travelled divided by the time taken,
and the time taken to travel a distance d at an average speed
s is d divided by s. If you stop a distance d km from Christchurch,
then the minimum time you should wait is the time it would take
you to catch up with the convoy just when it arrives in
Christchurch. So the time to wait should be roughly the difference
between the time for the convoy at average speed s to reach
Christchurch and the time for you at average speed (s + 5) to reach
Christchurch.

Specifically, Waimate is about 200 km from Christchurch.
Assuming the convoy has an average speed of 90 km/hr and you
want to travel with an average speed of 95 km/hr then you
should wait at least 5 times 200 divided by (90 times 95)
hours, that is, approximately 0.117 hours or 7 minutes.

As heavy trucks usually slow down considerably when going up
hills, if you are enjoying your coffee you should give it
another 5 minutes to be safe (but then again, the next convoy
could just be crawling past as you get back in the car).